The total number of pairs of vertical angles formed by five distinct lines that have a common point of intersection is: 10 pairs.
To find how many pairs of vertical angles are formed by five distinct lines that all intersect at a common point, we need to understand a few key concepts about vertical angles and intersecting lines.
Intersection Point: When multiple lines intersect at a single point, they form various angles at that point.Vertical Angles Definition: Vertical angles are the angles that are opposite each other when two lines intersect. They are congruent (having the same measure).Pairs of Intersections: Each pair of lines forms a set of vertical angles at the intersection point.Number of Intersecting Pairs: With five distinct lines, any two lines can form an intersection. The number of ways to choose 2 lines out of 5 to intersect can be calculated using the combination formula:
[tex]\binom{n}{2} = \frac{n(n-1)}{2}[/tex]
Where [tex]n[/tex] is 5 in this case.
Calculation: Plugging in the values, we get:
[tex]\binom{5}{2} = \frac{5 \cdot 4}{2} = 10[/tex]
So, there are 10 pairs of intersecting lines.
Vertical Angle Pairs per Intersection: For each of these 10 intersections, there is exactly one pair of vertical angles.
Each intersection of two lines forms one pair of vertical angles, and with 10 intersections, we have 10 pairs of vertical angles.
How many days are in a monthly billing cycle that ends on Feb. 13?
Answer:
31 days?
Step-by-step explanation:
There are 31 days from Janurary 13 to Feburary 13.
There are total 31 days in a monthly billing of cycle.
What is mean by Measurement unit?
A measurement unit is a standard quality used to express a physical quantity. Some of the measure units are to measure them.
Given that;
Last date for a monthly billing cycle is Feb 13.
Now,
Find the days for monthly billing as;
Since, Last date for a monthly billing cycle is Feb 13.
So, Its start with 13 Jan for monthly billing.
Since, There are 30 or 31 days in every Month of a year.
So, From 13 Jan to 13 Feb, it take one month for monthly billing of cycle.
And, It is equal to 31 days.
That's mean; There are 31 days in between 13 Jan to 13 Feb.
Therefore, There are total 31 days in a monthly billing of cycle.
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Which equation represents the line that passes through the points (-5,2) and (9,0)
Final answer:
To find the equation of the line passing through two given points, we can use the slope-intercept form of a line. The equation of the line passing through (-5,2) and (9,0) is y = -1/7x + 9/7.
Explanation:
To find the equation of the line that passes through the points (-5,2) and (9,0), we can use the slope-intercept form of a line, y = mx + b. First, we need to find the slope (m) of the line. The slope is given by the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, m = (0 - 2)/(9 - (-5)) = -2/14 = -1/7.
Next, we can choose one of the points and plug in its coordinates along with the slope into the equation y = mx + b to solve for b. Let's choose the point (-5,2): 2 = (-1/7)(-5) + b. Simplifying the equation, 2 = 5/7 + b. Subtracting 5/7 from both sides, 2 - 5/7 = b. Getting a common denominator, 14/7 - 5/7 = b. So, b = 9/7.
Finally, we can substitute the values of m and b into the equation y = mx + b to get the equation of the line: y = -1/7x + 9/7.
f(x)=−4x ^ 2 +10 {Find }f(-2)
Answer:
[tex]f(-2) = -6[/tex]
Step-by-step explanation:
Step 1: Set x to -2
[tex]f(-2) = -4(-2)^2 + 10[/tex]
[tex]f(-2) = -4(4) + 10[/tex]
[tex]f(-2) = -16 + 10[/tex]
[tex]f(-2) = -6[/tex]
Answer: [tex]f(-2) = -6[/tex]
Mike purchases a round wall clock the clocks radius is 10m what is the circumference of the clock
Answer:
62.8m
Step-by-step explanation:
Answer:
C = 20pi m or approximately 62.8 m
Step-by-step explanation:
The circumference is given by
C = 2*pi*r
= 2* pi *10
= 20 pi
We can approximate pi by 3.14
= 20*3.14
62.8
26)
If A represents the price of a t-shirt, which expression represents the total cost of 7 t-shirts?
A+7
A-7
Ax7
A÷7
Answer:
Ax7 is the answer
Step-by-step explanation:
yeah goodluck
Answer:
A*7
Step-by-step explanation:
There are seven shirts so the price is multiplied by 7.
could also be represented as A7
A bucket contains 50 lottery balls numbered 1-50. One is drawn at random. Find each probability.
P(at least 20 | prime number)
Answer:
For the prime numbers it's 15/50 or 3/10. For it to be at least 20 it's 31/50. For both to happen at the same time it's 7/15.
Step-by-step explanation:
The prime numbers between 1 and 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
50-19=31 so 31/50
The probability of drawing a prime number that is at least 20 from a bucket of 50 numbers is 0.2, or 20%.
Explanation:In this problem, you are being asked to find the probability that a number selected at random from a pool of 50, numbered 1 to 50, is both at least 20 and a prime number. In this case, let's first consider the prime numbers between 1 and 50, of which there are 15 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47). However, we are looking for prime numbers that are also at least 20. This leaves us with 10 prime numbers (23, 29, 31, 37, 41, 43, 47).
With these 10 prime numbers, and 50 total numbers to choose from, the probability can thus be calculated by dividing the number of successful outcomes by the total number of outcomes. Therefore, the probability P(at least 20 | prime number) is 10/50 or 0.2. This means there is a 20% chance of randomly drawing a number from the bucket that is least 20 and also a prime number.
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what is an equation that is a parabola with a vertex at(-1,-1)
of 100 patients that a nurse treat in one week 20 of them had the flu. what is the probability percentage that the next patient treated by the nurse will not have the flu?
Answer:
80%
Step-by-step explanation:
20% of 100 is 20, 100-20 = 80
What is the prime factorization of 200?
2 2 × 5 3
2 3 × 5 2
2 4 × 5
2 × 5 4
Answer:
2^3 * 5^2
Step-by-step explanation:
We need to break 200 down into prime numbers
200 = 20*10 These are not prime
= 4*5 * 2*5 The 4 is not prime
= 2*2*5 * 2*5 This is prime
Rearranging
= 2*2*2*5*5
= 2^3 * 5^2
Answer:
2 3x5 2
Step-by-step explanation:
What is an equation of the line that passes through point (8,0) and is parallel to the line x+y=5
Answer:
y = -x + 5
y - 0 = - (x - 8)
y = -x + 8
Step-by-step explanation:
The required equation of the line is y = 8 - x.
Given that,
To determine an equation of the line that passes through the point (8,0) and is parallel to the line x+y=5
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Given equation,
x+y=5
y = -x + 5
m = -1
Since the slope of parallel lines are equals.
So the equation of the line is given as, which is passing by (8,0)
y - 0 = -1 (x - 8)
y = 8 - x
Thus, the required equation of the line is y = 8 - x.
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Monique has five weeks to save at least $80 for a ski trip. Let n represent the amount she has to save each week.
Write and solve an inequality to find the amount of Money Monique needs to save each week.
Answer:
n ≥ 80/5
n ≥ 16
Step-by-step explanation:
please see the attached file for more explanation
Which ordered pair is a solution of the equation?
y-3=5(x-2)
A. Only 2,3
B. Only 3,2
C. Both 2,3 and 3,2
D. Neither
Answer
A only (2,3)
Step-by-step explanation:
If you graph it or plug it into Desmos that can also help
The ordered pair (2,3) is a solution to the equation y-3=5(x-2), but the ordered pair (3,2) is not. Therefore, the correct answer is option A: Only (2,3).
Explanation:In this Mathematics problem, we are asked to find which ordered pair is a solution to the equation y-3=5(x-2). An ordered pair is written in the form (x, y), so we'll test each option to see which one, if any, is a solution to the equation.
Let's start with option A, (2,3). If we substitute x with 2 and y with 3, we will have 3-3 = 5(2-2), which simplifies to 0 = 0. This equation is true, so the ordered pair (2,3) is a solution.
Next, we'll look at option B, (3,2). If we substitute x with 3 and y with 2, we will have 2-3 = 5(3-2), which simplifies to -1 = 5. This equation is not true, so the ordered pair (3,2) is not a solution.
Option C suggests that both (2,3) and (3,2) are solutions, but we've already established that (3,2) is not a solution to the equation.
So, based on our calculations, the correct answer is option A: Only (2,3) is a solution.
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Artie Works at Arby's. Last week he worked 22 hours. He makes $12.25 an hour. What was Artie's Gross Pay?
Can someone help me please
Answer:
$269.50 was Artie's gross pay
Step-by-step explanation:
12.25 (pay per hour) times 22 (hours worked that week) = $269.50 (gross pay)
According to the bar chart, what is the median of number of times a teenager reminded to do chores a week?
A) 1
B) 2
C) 3
D) 3.1
Answer: C
Step-by-step explanation: I did the math
The middle values are both 3, so the median is 3.
Option C is the correct answer.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
To find the median of the number of times a teenager is reminded to do chores a week, we need to arrange the responses in order from smallest to largest, and then find the middle value.
From the bar graph, we can see that the number of reminders ranges from 0 to 5, and the frequencies are not evenly distributed.
To determine the median, we need to count the total number of responses and find the middle value.
The total number of responses is:
2 + 5 + 8 + 14 + 7 + 4 = 40
Since there are an even number of responses, we need to find the average of the two middle values.
The two middle values are the 20th and 21st values when we arrange the responses in order:
0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5
Thus,
The middle values are both 3, so the median is 3.
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why didn't bob drink a glass of water with 8 pieces of ice
Answer:
IT WAS TO CUBED
Step-by-step explanation:
Round 56,291.8 to the nearest thousand.
Answer:
56,000.0
Step-by-step explanation:
The number 6 is in the nearest thousand. To round, you look at the number in front of the number you are trying to round and decide if that number is higher or lower than five. If the number is higher than 5, round up to the next highest number. If the number is lower than 5, the number stays the same.
Final answer:
To round 56,291.8 to the nearest thousand, observe the hundreds digit; it's 2, less than 5, so we keep 56,000 and replace subsequent digits with zeros, giving a rounded figure of 56,000.
Explanation:
To round 56,291.8 to the nearest thousand, we need to look at the hundreds place, which is 2 in this case. Since this is less than 5, we don't round up the thousands place. Therefore, we keep the number 56,000 as it is without increasing the thousand's value. However, since we are rounding to the nearest thousand, we replace the hundreds, tens, ones, and decimal places with zeros, resulting in the final rounded number being 56,000.
A class of 24 students visited a science museum. Each student paid the
museum’s admission fee and $ 6 for lunch at the museum. The class spent
a total of $ 336. What was the admission fee that each student paid? Please help me :(
Answer:
$8
Step-by-step explanation:
6×24=144
336-144=192
192÷24=8
8×24=1926×24=144192+144=336the admission fee was $8 for one student.
MRS.Bonnette's recipe for banana bread calls for 3 and one fourths cups of sugar. She wants to make 6.5 batches so that she has enough for everyone. How much sugar will she need
Answer:
[tex]21/ \frac {1}{8}[/tex]
Step-by-step explanation:
Since we're given that a batch requires 3 and one fourths cups of sugar, this is written as
[tex]3/ \frac {1}{4}[/tex]
If she wants 6.5 batches then we just cross multiply
1 batch=[tex]3/ \frac {1}{4}[/tex]
6.5 batches=x
X=[tex]6.5\times 3/ \frac {1}{4}[/tex]
X=[tex]6/ \frac {1}{2}\times 3/ \frac {1}{4}[/tex]
X=[tex]\frac {13}{2}\times \frac {13}{4}[/tex]
X=[tex]\frac {169}{8}[/tex]
X=[tex]21/ \frac {1}{8}[/tex]
Which of the following statements about the volume of a sphere and the volume of a cone are true? Select two answers.
A.
You can find the volume of a sphere with only the diameter.
B.
You can find the volume of a sphere with only the radius.
C.
You can find the volume of a cone with only the height.
D.
You can find the volume of a cone with only the diameter.
Answer:
Step-by-step explanation:
answer D would also be true
Answer:
Step-by-step explanation:
answer D would also be true
(X^-4)(x^10)=x^p
Help:(
Answer:
Step-by-step explanation:
[tex](x^{-4})*(x^{10})=x^{p}\\\\x^{-4+10}=x^{p}\\\\x^{6}=x^{p}\\[/tex]
Compare the powers, p = 6
How do you think inequalities are different from equations you have worked with before?
Answer:
Inequalities are different from equations. If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses.
In the diagram, which pair of angles are vertical angles?
Answer:
16
Step-by-step explanation:
What is 3(2 1/2) in repeated addition? HELP ASAP PLEASE!!
Answer:
7.5 or 7 1/2
Step-by-step explanation:
is -7x a monomial , a binomial or a trinomial
Answer:
Monomial
Step-by-step explanation:
A binomial has 2 terms(e.g. 2x + 3)
A trinomial has 3 terms(e.g. [tex]2x^{2} + 2x + 5x^{3}[/tex] )
Bo and Erica are yoga instructorsBetween the two of themthey teach 36 yoga classes each week11 teaches 12 fewer than twice as many as Bo, how many classes does each instructor teach per week?
Answer: The original price is $317.3885 or $317.38
Step-by-step explanation: Okay So first I went on google then I put
275.99 - 15% and got 234.5915 So then I put 275.99-234.5915 and got 41.3985 Then I put 275.99+41.3985 and got 317.3885 So the original price is $317.3885 or $317.38
I Hoped This Helped
Bo teaches 16 classes per week and Erica teaches 20 classes per week.
To find out how many yoga classes Bo and Erica each teach per week, we can set up a system of equations based on the given information.
Let B represent the number of classes Bo teaches per week. Let E represent the number of classes Erica teaches per week.
According to the problem, the total number of classes taught by Bo and Erica is 36:
Equation 1: B + E = 36
Also, we know that Erica teaches 12 fewer than twice as many classes as Bo:
Equation 2: E = 2B - 12
We can substitute the expression for E from Equation 2 into Equation 1:
B + (2B - 12) = 36
Simplify and solve for B:
B + 2B - 12 = 363B - 12 = 363B = 48B = 16So, Bo teaches 16 classes per week. Now we can find out how many classes Erica teaches by substituting B back into Equation 2:
E = 2(16) - 12
E = 32 - 12
E = 20
Therefore, Erica teaches 20 classes per week.
Thus, Bo teaches 16 classes per week and Erica teaches 20 classes per week.
Will give brainiest, please help, math 10 B unit 4 Lesson 3!
Answer:
Option choice A
or 3755.4 m2
Step-by-step explanation:
you multiply all the number together
What is the radius of a circumference of 1,017.36 units
so the answer is 161.85.Hope this will help u...:-D
Answer:
hope it helps uh........
how do you evaluate a logarithm
The steps to evaluate a logarithm.
- Identify the base of the logarithm.
- Rewrite the logarithm in exponential form with the base as the base of the exponent and the argument as the result of the exponentiation.
- Simplify the exponential expression.
- If the result is a fraction, simplify it if possible.
- If the result is a decimal or irrational number, use a calculator to get an approximate value.
What is a logarithm?A logarithm is a mathematical function that measures the relationship between the relative sizes of two quantities.
It is defined as the inverse of exponentiation.
That is, if [tex]a^b[/tex] = c then [tex]log_ac[/tex] = b, where a is the base of the logarithm, b is the exponent, and c is the result of the exponentiation.
We have,
To evaluate a logarithm,
Follow these steps:
- Identify the base of the logarithm.
- Rewrite the logarithm in exponential form with the base as the base of the exponent and the argument as the result of the exponentiation.
- Simplify the exponential expression.
- If the result is a fraction, simplify it if possible.
- If the result is a decimal or irrational number, use a calculator to get an approximate value.
For example,
To evaluate [tex]log_28[/tex].
Follow these steps:
- The base of the logarithm is 2.
- Rewrite the logarithm in exponential form:
2³ = 8
- The exponential expression simplifies to 8.
- No further simplification is necessary.
The exact value is 2³= 8.
Thus,
To evaluate a logarithm follow the steps above.
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Final answer:
To evaluate a logarithm, use the calculator's log button for the common logarithm or calculate 10 raised to the power of the logarithmic value for the inverse log. Logarithmic properties simplify expressions by converting multiplication into addition and exponents into multiplication.
Explanation:
Understanding and Evaluating Logarithms
To evaluate a logarithm, one can use a calculator's log button to find the common logarithm, which is based on base 10. If you have a logarithm and wish to find the actual number it represents, you take the inverse log of the logarithm. This can also be expressed as 10 to the power of the logarithmic value.
For instance, to evaluate log(100), you would press the log button on your calculator and then enter 100. The result would be 2, since 10^2 = 100. If you have the logarithm value, say 3, and want to find the number it corresponds to, calculate 10^3, which equals 1000.
Furthermore, logarithmic properties can be used to simplify expressions and solve equations. If you take the log of two numbers being multiplied, you can add their individual logs. Additionally, taking the log of a number raised to an exponent allows you to move the exponent in front of the log, thus multiplying the exponent by the log of the number.
During the seventeenth century, the principle of the logarithm was developed by Napier. Logarithms transform multiplication into addition, which simplifies many computations, like using antilogarithms and slide rules for multiplication.
A cylinder net is shown and the height is 10 inches high and has a radius of 2 inches. what is the surface area? Let π = 3.14.
a) 25 in2
b) 126 in2
c) 151 in2
d) 302 in2
Answer:
C
Step-by-step explanation:
find the area of the circles on the top and bottom with area of a circle being pie r squared
[tex]2(\pi 2^{2} )[/tex]=25.12
Find the area of the rectangle, with the height being one side and the circumference of the circle being the other
[tex](2\pi (2)) 10=125.6[/tex]
add the two together to get 150.72 and round
what is this???
-7(1-4m)=13(2m-3
Step-by-step explanation:
-7+28m=26m-39
28m-26m=7-39
2m=-32
m=-16